Sampling rate converters are used for converting input digital signals sampled at an input sampling rate into output digital signals sampled at an output sampling rate. In a conventional sampling rate converter, with a ratio between an input sampling rate R1 and an output sampling rate R2 being R1:R2=A·M:A·N=M:N (wherein A is a constant and M and N are relatively prime positive integers), the input sampling rate R1 is first converted into a sampling rate R3 that is the least common multiple of the output sampling rate R2, i.e., R3=R1·N=R2·M (upsampling). Next, samples in conformity with the output sampling rate R2 are extracted (downsampled) from a sequence of sample values which are N times larger than the input digital signals to obtain the output digital signals.
FIG. 10 is an explanatory view of a conventional method for converting sampling rates. Circles in FIG. 10 represent digital signals at the sampling rate R3. Among these circles, shaded circles represent input digital signals at the input sampling rate R1, circles of a thick line represent output digital signals at the output sampling rate R2, and white circles of a thin line represent signals other than the input/output digital signals.
The digital signals at the sampling rate R3 are calculated based on the input digital signals (upsampling). In upsampling, interpolation values are computed by using a finite impulse response low pass filter (FIR-LPF) which has a characteristic of blocking frequency components which are ½ or more of the output sampling rate R2. Then, out of the digital signals at the sampling rate R3, output digital signals at the output sampling rate R2 are extracted (downsampling).
Here, reduction in the sampling rate is referred to as downsampling. In the case of downsampling, the FIR-LPF is used to block high-frequency components of input signals and to suppress loopback noise caused by the reduction in the sampling rate. Contrary to this, increase in the sampling rate is referred to as upsampling. In the case of upsampling, it is not necessary to block the high-frequency components of input signals, but the FIR-LPF is used to compute interpolation values interpolated into positions different from the input digital signals.
FIG. 11 illustrates an impulse response of the FIR-LPF. The impulse response of the filter is expressed by the time function of a specified filter characteristics subjected to inverse Fourier transformation. When an impulse is input at time 0, an impulse response waveform is present around the time 0. In computation of interpolation values, an output digital signal at the time 0 is computed by using input digital signals in the range where the impulse response waveform is present. Although the impulse response waveform generally continues for a long time, the impulse response waveform is cut into a finite length of a fixed degree in consideration of practicality, and signal processing is performed therein.
In an actual converter, the time (negative time) to start an impulse response is set to 0 or a positive number. Specifically, start time−T of the impulse response is converted into 0, and the original time 0 is set to T for execution of sampling rate conversion. In digital signal processing, using a memory (shift register) enables such time shift processing.